~
---
I
'0
Deductive Efficiency + Belief Revision:
How they affect an ontology of actions and acting
I
Deep"
Kumar and Stuart C. Shapiro
Department
of Computer
Science
226 Bell Hall
State University of New York at Buffalo
Buffalo, NY 14260
kumard. shapiro~a.butTalo.edu
I
I
Abstract
The SNePS infere.nce engin~ i8 opti~zed.fo.r
deductive efficiency,
1.e., all bel1efa ~Ulred
VIa 1nference ue added to the agent'8 beh~fa BO tha.t fu1ure
queri~
~a.y be a.nawered b.y a retneva.l rather ~han
rederivauon.
An U8ump11on-bued
~rut~ m&1;nteDance IY8tem keeps track of the denva.t1on his to-
I
I
ries
of derived
chitec1ure
beliefa.
I
of
of
how
~ts;
precond1t1o~I,
and
the
effi-
addit1on,
~educt1ve
rulea,
acta)
Are
form
tenna
iu
Each formula.
il
The
the
Introd
proposition
called
SWM,
uction
repr_nt.ed
SWM,
SNePS
underlying
denotes
numbers
used
a belief
for
nod~
logic
and
of
by
the
all
SNePS.
o! the Alent
formulas
and
a.re names
SNePS nodes. The excla.ma.tion
indica.tes tha.t the agent currently
represented
.supported
the logic
uaing
the
in the example
numbered.
pla.n decompos1t1ons.
node.
"1
of
mArk (!)
believes
and
K22 ue
aiD.. (Swff8) which form the basic objecu
of
underl.ying
the infer~nce
and belie! re--:is~on
I.em
the
proposition8
the
agent
Traditionally
systems
beliefa
co~jure
and
the1r
truth
up
maintenance
ima.ges
subsequent
~e-
bellef
,
or,
In
some more adventurous
cases, reasoning
about the future, as
'
"
,
'
d
'
d
'
in a pliLnnrng sltua.tlon;
or, rn a. pla.nnlng
omaln,
etectrng
al
d
r
I
ed
I
.
,the
InconsIstences
In an
rea. y ,ormu
a.1.
p a.n, or, more
tYPIcally, reasoning about the b~li~fa of other agents. SN~BR. the
SNePS system for belief reVISIon [MartIns
and ShapIro 1988]
'
an
,
bee'n
used
for
some
part
of
SNePS
of
I.lIese
2.1
tasks.
[Sha.piro
It
and
forms
Group
1989,
Shapiro and Martins
1989]. i.e. any~ne working
wit~ SNePS
hu at their disposal a.t least the facull.y ~f an A,~MS (l.e. contradiction
del.~tion
and subsequen~ belIef revI810n!. It turns
of the inference
2
To illustrate
&S5ume
The
SNePS
Inference
BOrne of the fea.tures
that
I.he Alent
has
following
inference
hypol.h~
the
and
agent
form
II uked
the
?
g
d ch
b ~war
--I-
.,
IJn1ng
t
'
IS a bl e to ded uce
ag ent
h
roug
h th
1
ted b
e ru e represen
y
K1
A is a support,
which
is
Note
thaI.
represented
the
by
&gent
the
h&8
proposil.ion
now
K53
added
the
(see
newly
Figure
2).
derived
be-
lief to its current
belief space along with the origin
tag of
der and a.n origin set containing
the hypotheses
K1 and K22
indicating
that these were used in il.s derivation.
D d
3
one g~ts
Engine
of the SNePS
I.he
1 are
When
o
Em
d B
0
1
0
f R
. 0
er
h
engine"
toget
all
y,
A
actIng.
dd
efficiency
viable alterna.tives
1.0overcome ~he STRIPS
assumpt,lon whue
modeling
agents that I.C~. Th18 pa.per present8,evldence
of
some of"~bese nol. so obvlo~s
results that we claIm denote a
partIal
IntegratIon
heaven
(term {rom Pa~l Roeenbloom),
First we presenl. an ~xam,ple of the SNePS In~erence engine
I.nd the TMS operat,lonl
In~olved.
Then we dIscuss our decilion8 I.bout deductIve
effic1ency.
Then we present proposlI.ion&! representa.l.ionl
for planning
a.nd I.cl.ing aff~ted
by the
presence of deductive
efficiency
and belief revision.
gine.
'
US1n
.
and
plannrng
for
resentatlons
the deductive
Figure
space.
IS a support.
of the presence of such an 1ntegrated
to simplify
certain propositional
rep'.
with
,
Itlon
.
,
I
What
"
inl.egra.!
in
I. bellef
query
~f, detecti~n
reV1810n;
8how~
'8 curren
evision
revision)
arise
Ie
agent.
m,ay
a cons18tent
e
belief
modeled
I.hal.
to guaranl.ee
an
of the
incon8istencie8
and
clency
space
informa.tion
uctlve
so a.s 1.0 del.ecl.
of new
e
(TMS)
ca.use
out thaI. I.he guarantee
ATMS can be exploited
I
,
tionl,
nodea
the corresponding
alter a node name
I
I
Ar-
8Yltem.
Asaociated
w1th each 8wff 1S a IUpport contalnrng
a.n origin togwhich i8 hyp for bypotbeBeB,
and der for derived IWff8i a.n origin
letwhich contains
thC»e (and only
thC»e) hypotheses
used in the deriva.tion
of the Iwffi and a
~..triction
.set-wbich
record. inconsistency
in!ormal.ion.
All
beliefa o! I.be agent reside in a. beliej.spoce which is a set of all
I.he hypotheses
and all the 8wffs derived
from them.
Thus,
has
I
.~
pr.o~t1onal
.ciency o! th~ basic sY8tem au tomat1cal~y
exte~ds
Itself to effiae~t, search o! plan8, and hleruch1cal
of contradicting
I
I
Iuch
of
which Are repr~nted
u SNePS propositiou
K22a.nd K1 (.ee
Figure 1). In tm. pa.per we a.re ~ng
a liDea.r predica.1e-logic
notation
to illuatra.te
the exa.mples.
In reality,
1he propo.itiou
a.re repr~nted
U aema.ntic network
nodes. The nol.&1ion uaed in 1he pa.per ma.y a.ppeAr u a. hiper-order
logic.
However,
remember
tha.t all eDtiti~
(individuall,
propo.i-
SNIP,
the
SNePS
inference
packa.ge [Hull 1986, Pinto-Ferreira.
et 01. 1989] is optimized
for deductive
efficiency,
i.e., all beliefs acquired via inference
a.re added 1.0 the agent's belieu so I.ba.1.ful.ure queries ma.y be
a.nswered bv a. retrieval
ra.l.ber tha.n rederiva.l.ion.
Of course, il.
is imperati~e.
I.hen. to have a built-in
trul.h majnl.enance
sys-
(or
I
8how
ontology
pla.n8;
In
1
I
.
1he
actions.
I
I
We
limplifies
representa1ionl
effects
I
A is a block.
All blocks are supports.
en-
beliefs:
In the exa.mple
the a.gent will
continue
to believe
M53
as long as the beliefs Ml and M22 are held.
If the earlier
query is repeated
the I.nawer is retrieved
(i,e. A is a support)
by limply
looking
at the belief 8ta.tU8 of M53. Tbis i8 what we
mean bv deductive
efficiency,
i.e. the inference
engine does
not re~a.t
the inference
process used in deriving
M53 8ince
it had already derived it eArlier and its origin leI. still holdl.
A derived
proposition
i8 au1oma.~ically
removed
agent'.
belief 8pace if a.ny ODe of the hypotheses
from the
contajned
in iu origin let il removed.
AI beliefa of the agenl. change
beca.use of action.
this providea I. built-in
mechanism
for reviling
a belief space alter an action i. performed.
All that
needl1o
be done by the Alent alter executins
an action il to
perform
93
above,
the
acts
of believing
the
action's
consequences
which
~
--
.-
No.: FormulA
Suppor\.
< hyp,{M22!}, {} >
M22!: lu(A.BLOCK)
M1!: Vx[lu(x,BLOCK)- 1u(x.SUPPORT)J
Filure
< hyp,(M1!),{~-~
1: M22: A is I block. M1: All block, Ire 5UPPOI'U_-
No.: FormulA
< hyp, {M22!}, {} >
M1!:Vx[lu(x,BLOCK)-lu(x,SUPPORT)J
MS3!:lu(A,SUPPORT)
<hyp,{M1!},{} >
<der,{Ml!,M22!},{} >
.
involvel adding or deleting oChypo\.hesesdirectly relAted to
that the block iI held (MB). Filure.
\.he ac\. performed. SNePS provides two operationsIdd-tocontextI.he
and
remove-from-context
to add or remove hypotheses
from
&gent'.
bdieC space.
space &fl.er the effects oC the loCI.oCpicking up a block are &110
added.
..
~elief& oCt~e a~ent change frequently during acl.ing. ~very
if for some reason M 1 (or M22) was removed from the &genl.'I
belief space (using remove-from-context). M53 would &Iso be
removed. A\. a lal.er time if M1 (or M22) i& &gain added 1.0
the &gent '& belief Ipace, M53 is automatic&lly replaced. Thus
maintaining deductive efficiency.
.
.
. effiCIency,
.
The combination
of above three feal.urel (deductive
time an action 1&performed the world changel. Accordingly,
the &gent'& beliefs about the world Ihould &150change. Typic&lly, effects of a.n action (represented as STRIPS-ltyle
ope:rator& [Fike! and Nil5lO~ 19:1J) are .pecified as .add-dele~e
llst& so that after the actIon IS performed the belief .pace IS
upda.ted by using
the operator'.
&dd-delel.e lilt, Traditiona.l
A STRIPS
a.IIumption
underlie!
such implementation&,
.auto~a\.ic revi~ion of ~he ~lief &pace, and a~l.omatic reI~cluslon of,de~lved b~lIefs) In an ATMS-,based Infere~c~ englne has a ~Ignltica.nt Infl~ence on the. desIgn of proposILI~na.J
repres.enl.~tlons for pl.a.-nnl.nga.nd acting and Lhe mechanIsm
of acLlng ILself. We will dIscuss the!'e nexL.
schemes for using an ATMS for a.n acting .ysl.em rec_ommend
that effecl.& of performing action& Ihould only be added a.nd
a consistency maintenance function applied to del.ecL incon&i8tencies in the belief space, and 8elecL an appropriate set
of beliefs to be removed 80 u to mAke the belief space con-
"
t
ro p os1 lona
o
1R
0"
Act1ng
and
Belter
0
0
Rev1s10n
siltent [Drummond 1987]. While belief revision sysLems are
built to detect incon5iltencies, a.utomated selection of beliefs
.",
to be removed 1&not a. vIable option. Typlc&llyan
ATMS, as
doe! SNeBR, enters a di&log with the user 80 that the user
ca.n select the beliefs to be removed upon detecLion of some
incon&istency.
t t"
r
epresen
a lons lor
.
actlons
\\.e will presenL an overvi~w of our representations of a.ction~ Lhrough an exa.mple. See [Kumar a.nd Shapiro 1991a,
J\umar and Shapiro 1991b] for more deLa.ils. Con&ider Lhe
block&world acLion of picJ.:jng up a blocK. We inform the
agent abou\. \.h~ action by tirs\. saying
In the SNePS a.cting sYltem we define two mental a.ctions~ELIEVE a.nd DISBELIEVE, t.hat ,ue used 1.0 upda.te the belIefs of the &gen\. &fter an actIon 1&performed. The effecLory
componen\.s of the I.wo actions are the operations add-tocontext and remove-from-context respectively, The TMS facilitates automaLic revi&ion of the belief space after a hypothesis
is removed as a result of 5Ome DISBELIEVE a.ction (&II derived beliefs having the disbelieved hypothesi& in their origin
All blocks are supports
Picking up is a primitive action.
.
.
, .
whIch .resuJLs In the pro~<:>sltlons represented by M1 a.nd M2
(~ FI.gure 3), Precond!tlons of a.cL&are also represented a.s
proposItIons. Thu& the Input
Bf
. k.
bl k h bl k
b I
e ore piC Ing up a oc t e oc must e c ear.
ed
.
I
.f '
d '.
f
. .
IS Interpret
a.sa generic ru e &peC1
Ylng a precon Itlon or
pi.cking up a block. The rule i& repr~nted by. no~e M3 in
FIgure 3. I\. could be paraphrued 1.&, For &11x, If x IS a block
then Lhe act of picking up x ha.s Lhe precondition tha.l x is
clear." Effects are .imila.rly represented. Thus the following
set are also removed). This implements the utendedSTRIPS
a.IIumption [Georgeff 1987]. For example, if the &gent'&belief
&pa.ceis that of Figure 4 and it is I.old
After picking up a block the block is not clear and the block is
h~ld.
the a.cting system infer& the propc:.il.ion&
A is I block. A is clear.
which get represented by nodes M22 and M23 re!pectively in
Figure 5. and asked to perform the a.ct
I
I
I
I
...
I
I
I
I
I
I
I
Pick up A.
A precondition of picking up A is that A is clear.
An effect of picking up A is that A is no longer clear
An effect of picking up A is that A is held.
is represented by two ruJes- one specifying the effect that
Lhe block is no longer clear (M6); and the other specifying
94
~
show. the &gen\.',belief
Anol.her important efficiency criterion incorpora.l.edin the de5ign of I.he SNePS inference engine i& automal.ic re-inclu&ion
of derived belief&inl.o the currenl. belief &paceif &11oCI.he hypo\.hesesin \.heir origin se\.come 1.0be included. For exa.mple,
5
:I
.I
Filure 2: M22: A is I block. M1: All block, Ire IUPPOI'U.MS3: A is I 5Upport.
P
I
'
Suppor\.
M22!: lu(A, BLOCK)
4
-
I
I
I
~
.
~~~~
I
No.: Formula.
I
Ml!:
~
Vx[15a(x, BLOCK)
1
I
< hyp,{Ml!}, {} >
-
< hyp,{M2!},{} >
< hyp,{M3!}, {} >
ActPrecondition(PICKUP(x),Clear(x»)]
clear.
No.: Formula.
""--'Ml! : Vx{lu(x, BLOCK)
Support
.
- 'sa(x,
SUPPORT)]
--
..-
M2! : lu(PICKUP, PRIMITIVE)
M3! : Vx(lsa(x,BLOCK)
1--M6!:Vx(lsa(x,BLOCK)
I
I
- Isa(x,SUPPORT)]
M2!: lu(PICKUP,PRIMITIVE)
M3!: Vx[lu(x, BLOCK)
I
I
Support
ActPrecondition(PICKUP(x),Clear(x»)]
ActEffect(PICKUP(x),..,Clear(x)]
.1
I
I
I
.,
< hyp,{Ml!}, {} >
< hyp, {M2!}, {} >
< hyp,{M3!},{} >
< hyp, {M6!}, {} >
Figure 4: The SNePS representa.tion of the a.ct of picking up a.block. (Ml: All blocks are supports. M2: Pickinl up is a pl'imit~
action. M3: Before picking up a block the block must be clear. M6: After picking up I block the block i5 not clear. M8: After
picking up a block the block the block is held.)
-Support
~o.: Formula
Ml! : Vx[lsa(x, BLOCK) -
1
,- ---,
Isa(x, SUPPORT)]
M2! : Isa(PICKUP, PRIMITIVE)
M3! : Vx[lsa(x, BLOCK) - ActPrecondition(PICKUP(x),
Clear(x»]
M6!: Vx[lsa(x,BLOCK) ActEffect(PICKUP(x),..,Clear(x))]
M8!: Vx[lsa(x, BLOCK) - ActEffect(PICKUP(x),
Held(x))]
,-"M22!: Isa(A, BLOCK)
-
~\M13!:Clear(A).
< hyp, {Ml!}, {} >
< hyp, {M2!}, {} >
< hyp,{M3!}, {} >
< hyp,{M6!}, {} >
< hyp,{M8!}, {} >
< hyp,{M22!},
{}
>
<hyp.{M23!},{} >
< der, {M22!,M3!}, {} >
< der, {M22!,M8!}, {} >
< der, {M22!,M6!}, {} >
M26!: ActPrecondition(PICKUP(A),Clear(A))
M29!: ActEfTect(PICKUP(A),Held(A))
M30!: ActEffect(PICKUP(A),..,Clear(A))
supports. M2: Picking up is a primitive action. M3: Before picking up a block the block must be clear. M6: After picking up a
block the block is not clear. M8: After picking up a block the block the block is held. M22: A is a block. M23: A is clear. M26:
A precondition of picking up A is that A is clear. M29: An effect of picking up A is that A is held. M30: An effect of picking up A
is that A is no longer clear.)
I
I
I
No.: Formula
Ml! : Vx[lsa(x. BLOCK)
Support
.- -.
- Isa(x,
SUPPORT)]
M2!:lsa(PICKUP,PRIMITIVE)
M3! : Vx[lsa(x, BLOCK) - ActPrecondition(PICKUP(x),
Clear(x))]
M6! : Vx[lsa(x, BLOCK) - ActEffect(PICKUP(x),..,Clear(x))]
M8!: Vx[lsa(x, BLOCK) - ActEffect(PICKUP(x),
Held(x))]
M22!: Isa(A, BLOCK)
M26! : ActPrecondition(PICKUP(A),Clear(A))
M29!: ActEffect(PICKUP(A),
Held(A))
I
..
I
.
M30!: ActEffect(PICKUP(A),-.Clear(A))
M28!: -.Clear(A)
M27!: Held(A)
<
<
hyp,
hyp,
1M3!},{} >
{M6!}, {} >
< hyp,{M8!}, {} >
< hyp,{M22!}, {} >
< der, {M22!, M3!}, {} >
< der, {M22!,M8!},{} >
< der, {M22!,M6!}, {} >
< hyp,{M28!}, {} >
< hyp,{M27!}, {} >
Figure 6: Belief spa.ce of the a.gent a.fter the a.ct PICKUP(A) is performed (Ml: All blocks Ire 5upportS. M2: Picking up is a
primitive action. M3: Before picking up a block the block must be clear. M6: After picking up I block the block i5 not clear. M8:
After picking up a block the block the block is held. M22: A is a block. M26: A pl'econdition of picking up A is that A is clear.
M29: An effect of picking up A is that A is held. M30: An effect of picking up A it that A it no longer clear. M28: A is not clear
M27: A is held.)
I
I
..
< hyp, {Ml!}, {} >
< hyp,{M2!},{} >
95
.
which ~ lepl~Dt.ed
by .ods M26, M30 _d M29 18pecLively (Figure 5). SiDce the p~diLiOD
ia 8a.1isied (i.e. the
Two t~
~La.boD
.
ageDt belie'98 M23) tbe actoiODwill be ~t.ed
~~
aILer the aceDt will perform tbe acta
~OD~.
BElIEVE(HeId(A))
DISBElIEVE(Clelr(A))
'
.
. '.
of belleY1Dgthe effecta (tDdiat.ed by bdiefl ~3~, M29).
Tbe eff~r
a>mpoDent of the mea\&J act of belieY1Dg(BELiEVE(p)) ia impleme.ted uiDg remow-from-context on "'p
aDd add-to-context on p aDd DISBElIEVE(p) ia ~mOYe-fr~
open.&or, unst8Ck [Nil8OD IPSO], waich ia .-&1ural. Thul,
Bot oDly do we elimi.a.t.e 'be Deed {or opera.1on u ~p&ra.\.e
.-
_d
tbe~
are ill~.by
tkia ~~e:-
of a>D~UYe
eft"ect
of deriged pro~Lio~
tha.1tberep~
l.nY1al; _d
caD .~ acAieged by tbe belief
Tbe fonDer, lD &.radi~al
STRIPS style reJ>-
~La.1iou of thebloa-orld leqmfataerepraeDt.&Liou
-Lama.LIC
{or actoiou, we a18O_d
of - extra
.p with (ewer, aim-
pier, _d at the aame Ume more .u8&tile rep~ta.1.iODI for
actiou. Tbe latter (automatic belief reMOD by removal of
deriged prop<)8itiou) impiemeD&.athe e%tendedSTRIPS uavmption,
context on p aDd Idd-to-context OD "'p. Thu aILer the act ..
performed aDd itl effecu belieYed, we will ha.e the reYi8ed
I!. in
belief 'p&a ahown in FiJure 6.
fect remoYedearlier will automatically be re-1DclDded.Thll
,
.
'
.
a fDture ait~ati°n.'
A iI on B~ the a>Dt.ex~epeDdent
way of ,pecifyiDg a>ntex\-depeDdent
effect.- ~
e~-
to be bet-
ThiJ; example 1l1uatrat.e8o~e of the ad~I.a.gS of dedudin
effiaenc:y employed by t~e.lDfereDceenpDe-- ODtethe. acent
hu. denved the ~recoD~tlOU ud effecta of ~rlo~ng
-:n
acUODon a ,~fic
object they become ~enYed beliefl l.n
t~e agent', belief apace, heDce ~uture retne.Yal of pr:eco~ditlonl/effectl
of the lame ~ W111
Dot z:eqwre reden~~on.
(I.e, ... long u the uaumptloDI,underlYl.Dg the propO8luou
M26, M29 a.nd M30 hold, they WIll be believed, The uaumJ>tions being M3 and M22 for M26, MS, M22 for ~29, .and M6,
M22 for M30. As ,lOOn u the, agent corns to diI~leYe ,uy
on~ of th~ underlYing uaumptlons, the c;orrea,pondingdenYed
?elle£. -:111be removed from the, ~ent I belief IPace" Thus,
\er thu that uaed by SIPE [Wilkiu IPS8] {or 8eYeralreuonl.
For ODe,we han elimiAa.1edthe Deed{or aleparal.e apecification of actiou u opet'ator.. In SIPE, a>Dtex\-dependeDteffecta are rep~nted by domain rvJeoI,While domain ruls of
SIPE help to make the operators more applicable the applicability of the domain ruls them8elys (u a rep~ntation
of a
aual theory) ia not uniform in SIPE. ID our repre8enl.ationl
the 10 called traditional operator il conltrucl.ed dynamically
at the time of acting, i.e, each time IJI act il performed. its
preconditions aDd effec&.aare deduced. Coupling deductive
efficiency with belief-revision provides a more natural, yet efficient, way of representing actions, a.nd at the lame I.ime, a
If an action hu any context-sensitive
the condition
qualifying
the context
more uniform
effects, we CIJI Include
in the IJItecedent
part
of the rule specifying the effects, This is preaenLed next,
of a auaal
C
5,1 Context-senlitive
effects
I n a worId were
h blU\:Aa
--I..d -_.J
th r 11 .
are con51 e~ luppor_,,.
e 10 oWIng
..
_I ff t
-_.J
b
.fi -.J f
. _\..:
bl k.
-AU
.JdItlonAJ
e ec s n=u Lo e spec cu or pl~ng up a oc,
If a bl.ock is on a support then Ifler picking, up the block the
block IS not on the support Ind the support IS clear,
The belief apace after the above two propositions
nol.ion
IJId
B is a block.
A i$ on B.
.
..
..
a!e ad~ed to the b:lIef spaceof Figure ~ ISshown In Flgure 7.
theory.
. ,
..
An effect of p~ck~ng up A ~ thlt
An effect of pickIng up A '$ that
, .
precondItions
have beliefl a.bout. So, plana, once derived will be believed
'..
by the -.gent u long AI their underlYing I.IaUmptlonl are be_1
1... d -.J
1. _.J Th
.
1..- _.J
leycu.
e agent CIJI AJIO uc proVl = zenenc p~pac&Ag=
abst~&Ci .plul that form I.,he -.genl. 's pllJl library. Before indulglng In a pllJl genera.tlon phase, I.he agenl., when uked
to do IOmething, cu retrieve lpecific piau from the plana it
already hu belie£. about. We have pr°po,ai.tional repr~n-
tations for pla.ns that rep~nt
decompositions of complex
actions... well u thc.e that apecify ways of achieving goals.
The repr~ntationl of pla.nsa.r:edefined in I.ermsof primiti ve
control actions which, in our repertoire, iDclude sequencing,
conditional, ud iterative actl (among others),
like the aimple one below
I
'
I
I
I
I
I
8
I
I
If a block is on I 5UPport then I plan to achieve that the 5upport
is clear is to pick up the block Ind then put the block on the
A ~ no longer on B.
B IS clear.
w~ich are represented by de~iYed propositions
(Figure 8 shows the Dew belief space).
I
d't '
6
on 1 lona I PI ana
Like acta,wetreat plus u mental entitis I.ha.tthe ~ent can
R~l.rieval of plans, limila.rly, benefiu !rom the deductive effi.
ciency of the inference engine. Additionl.lly,
conditional plans
,
. .
the agent will deduce two addItIonal
I
.
~~XL, If the agenL IS now requested to
Pickup A.
-
b'talC,
M35 and M36
Howeyer, th~
propositions hold only in I.he cue where A is
on B. Notice that the origin 8ets of M35 IJId M36 contain the
hypol.heses MI, M2I (which were used to derive M34), M22,
a.nd M24. After the act is performed the mental actions
BELIEVE(Held(A))
DISBElIEVE(Clear(A))
BELiEVE(Clelr(B) )
DISBELIEVE(On(A, B))
cu be repr~nted,
u in the case of context-8en&iLiye ~ffec\.s,
by specifying the qualifying proposil.ion5 ... u~ents
of
the rule specifying the plan. i.e.
yo
x,y [Isa(x, BLOCK) Isa ( y, SUPPORT)
-
"
" 0 n(x,y )
the agenl 's belief space. Since M35 a.nd M36 cont&1n M24
in their respective origin 8eU th~y are also removed. The
revised belief space after this is shown in Figure 9,
96
'
I
GoaIPlan(Clear(y),SEQUENCE(PICKUP(x), PUT(x, TABLE)))]
Once -.gain, in a situation where A il on B, to clear B the.
agent will use the above rule to derive
will beperformed,
Thelut mentalacl.ion
removes
M~4from
I
A plan to clear B is to first pickup A Ind then put A on the
table,
."
...
whlclJ IS a denved proposItion haYln.g the quallfYlng 5IlU~.
\.ion On(A, B) u one of il.s Ioaumpl.lons. Once the plan IS
executed it will no longer be bdi~yed. II will, u usual, be
.
.
.
8
I
I
I
:t44.t
.
I
I
1
.
~~
~
.
't-i
~'
,~..,.~,.,--~
,,--,~
'"' ~
1: .;,;..,;...
'
~.
---"--
,
.
No.: Formula.
Support
Ml!: Vx{lsa(x,
BLOCK)- lu(x,SUPPORT)]
--.
< hyp,{MI!}, {} >
M2!: Isa(PICKUP,PRIMITIVE)
< hyp,{M2!}, {} >
M3!: Vx(lsa(x,
BLOCK)- ActPrecondition(PICKUP(x),Clear(x))]
< hyp,{M3!},{} >
M6!: Vx{lsa(x,
BLOCK)
- ActEffect(PICKUP(x),-.Clear(x))]
< hyp,{M6!}, {} >
M8!: Vx{1sa(x,
BLOCK)- ActEffect(PICKUP(x),
Held(x)))
I
I
;
I
I
< hyp,{M8!}, {} >
M22! : Iu(A, BLOCK)
M23!: Clear(A)
M9! : Vx, y(lsa(x, BLOCK)" lsa(y, SUPPORT) "On(x,y)
< hyp, {M22!}, {} >
< hyp, {M23!}, {} >
MI0! : Vx, y(lsa(x, BLOCK)" lsa(y, SUPPORT) "On(x, y)
< hyp,{MI0!},{} >
M2l!:Iu(B,BLOCK)
M24!:On(A,B)
<hyp,{M2l!},{} >
< hyp,{M24!},{} >
-
ActEffect(PICKUP(A),-.On(x,y)))
< hyp,{M9!}, {} >
- ActEffect(PICKUP(A),Clear(y))]
5UPPorU.M2: Picking up i5 a primitive action. M3: Before pickinK up a block the block mu5t be clear. M6: After picking up a
block the block is not clear. M8: After picking up a block the block the block is held. M22: A is a block. M23: A is clear. M9: If
a block is on a 5upport then an effect of picking up the block is that the block is not on the support. If a block is on a 5UPportthen
an effect of picking up the block is that the support is clear. M2I: B is a block. M24: A i5 on B.)
I
I
No.: Formula
I
Support
MI!: Vx(15a(x,BLOCK) - Isa(x,SUPPORT)]
M2! : Isa(PICKUP, PRIMITIVE)
<
1
M3! : Vx(15a(x. BLOCK) M6! : Vx(lsa(x. BLOCK) -
< hyp, {M3!},
< hyp, {M6!},
I
M8! : Vx(15a(x,BLOCK)
ActEffect(PICKUP(x),
Held(x»]
M22!:lsa(A,BLOCK)
M23! : Clear(A)
M26!: ActPrecondition(PICKUP(A),Clear(A))
M29!: ActEffect(PICKUP(A), Held(A))
M30!: ActEffect(PICKUP(A),-.Clear(A)
M9! : Vx, y(lsa(x, BLOCK) A Isa(y, SUPPORT) A On(x, y)
ActEffect(PICKUP(~,-.On(x,y))]
I
-
I
I
I
I
{} >
{} >
< hyp,{M8!}. {} >
< hyp,{M23!}, {} >
< der, {M22!,M3!}, {} >
< der, {M22!,M8!}, {} >
< der, {M22!,M6!}, {} >
< hyp,{M9!}, {}
- ActEffect(PICKUp(~,Clear(y))]
<hyp.{M24!},{}
Isa(B,SUPPORT)
>
< hyp,{MI0!}, {} >
< hyp,{M2l!}, {} >
M24!:On(A,B)
<
der,
{M2I!.MI!},
>
{}
>
< der, {MI!, M2I!. M22!.M24!}, {} >
< der,{MI!, M2I!, M22!,M24!},{} >
M3S! : ActEffect(PICKUP(A),-.On(A, B))
M36! : ActEffect(PICKUP(A),Clear(B))
Figure 8: Belief space alter the preconditions &lid effects of PICK
up is a primj~iv~action. M3: Before picking up a b~ck the block m~st be clear. M6: Af~er picking up a block the. ~Iock is ?ot. clear.
M8: After pICkingup a block the block the block IS held. M22: A ISa block. M23: A ISclear. M26: A preconditIOnof pICkingup
A "81 that A i5 clear. M29: An effect of picking up A i5 that A is held. M30: An effect of pickinc up A "81that A is no longer clear.
M28: A is not clear. M9: If a block is a 5upport then an effect of pickinK up a block i5 that the block "81no IonKeron the support.
MI0: If a block is on a 5UPportthen an effect of picking up a block is that the support is cle.r. M2l: B is. block. M24: A is on
B. M34: B is a 5upport. M3S: An effect of picking up A is that A is not on B. M36: An effect of pickinK up A is that B is clear)
I
-
{MI!}, {} >
<hyp,{M22!},{}>'
-
M34!:
.
ActPrecondition(PICKUP(x),Clear(x»)]
ActEffect(PICKUP(x),
-.Clear(x))]
MIa! : Vx,y(lsa(x,BLOCK)A Isa(y,SUPPORT)"On(x, y)
M2I!: Isa(B,BLOCK)
hyp,
< hyp, {M2!}, {} >
97
~;,~"
'.
No.: Formula
,
M1!:Y'x{iII(x,BLOCK)-ka(x,SUPPORT)]
M2!: ka(PICKUP,PRIMITIVE)
1I8(x, BLOCK)
M3! :
~
~
.~~~
Support.
<hyp,{Ml!},{}
>
< hyp,{M2!}, {} >
< hyp, {MJ!}, {} >
- ActPreconditK>n(PICKUP(x),Clur(x»)]
< hyp,{M6!},{}
M6!:V 118(x,BLOCK)- ActEft"ect(PICKUP(x),...clur(x)]
M8!:V
118(x,BLOCK)-
M22! : iII(A,
< hyp,{M8!},{} >
ActEt:ect(PICKUP(x), Held(x))]
< hyp, {M22!}, {} >
BLOCK)
< der, {M22!, M8!}, {} >
< der, {M22!,M6!), {} >
- ActEt:ect(PICKUP(A),...on(x,y))]
< hyp, {M9!), {) >
MID!: Vx,y[lu(x, BLOCK) A lu(y, SUPPORT) A On(x,y)
- ActEt:ect(PICKUP(A),Clear(y»]
M27! : Held(A)
< hyp,{MID!), {)
<hyp,{M21!),{}
< der,{M2I!,M1!}, {}
<hyp,{M37!},{}
<hyp,{M38!},{}
< hyp,{M28!}, {}
< hyp,{M27!}, {}
>
>
>
>
>
>
>
Fi~ure 9: Belief Ipa.celiter the act PICKUP(A) ia performed (Ml: All blocks Ire supporu. M2: Picking up ill primitive action.
M3: Before picking up a block the block must be clear. M6: After picking up I block the block iI not clear. M8: After picking up
a block the block the block j5 held. M22: A is I block. M26: A precondition of picking up A iI that A i5 clear. M29: An effect
of picking up A j5 that A j5 held. M3D: An effect of picking up A i5 that A j5 no Ion~er clear. M9: If I block i5 a support then an
effect of pic.kingup a block j5 t.hat the block is ~o longer on the 5uP'p°rt. MID: If a block ~son a support then ~n effect of picking
up a block .5 that the support IS clear. M21: B .5 a block. M34: B IS a 5Upport. M37: A .5 not on B. MJ8: B .5 clear. M28: A is
not clear. M27: A i5 held.)
re-included in the belief apaceif a simila.r situation (i.e. A is
on B) il attained. While preconditions of pll.M CI.JIbe del.lt
by specifying them in the antecedents of rules, pla.nl tha.t include condition&! a.cuonl still use condition&! control actions
(See [Kuma.r a.nd Shapiro 1991b]) as part of the pla.n.
7
Work.hop, pagel 189-212, Loe Alt~, CA, 1987. AAAI I.JId
CSLI, Morgl.Jl Kauffma.nn.
[Fikes a.nd Nilaon 1971] Richa.rd E. Fikel a.n~ N~lI J. NilsIOn. STRIPS: A new a.pprol.ch to the a.ppllCl.tlon of tbeorem proving to problem .olving. Artificial Intelligence,
5:189-208,1971.
Remarks
[Georgeff 1987) Michael P. Georgeff. Planning. In Annual
Review. of Computer Science Volume !, pages 359~DD.
AD.Du&!Reviewl Inc., Pl.lo Alto, CA, 1987.
A basic premise of our approach Items from the empiric&! obaervation tha.t, typic&!ly, good knowledge representation a.nd
reuoning systems are ba.d ca.ndida.tesfor pla.nning/acting
modeling and vice verla.. If one wishes to extend a good KR
system for pll.Jlning/acting modeling one ca.n take the easy
way out by simply integra.ting a. mutu&!ly exclusive off-the-
I
I
I
[Kuma.r and Shapiro 1991a.] Deepa.k Kuma.r and Stua.rt C.
Sba.piro. Ardlitecture of I.JI intelligenL ~ent in SNePS.
a.t t~e 5a.me ~Im.e prea.rchltecture II 51mple,
SIGART
more uniform, and offers via.blesolutions to some of the standa.rd .problems. I.n this paper we ba.vet~ed to .demonstra.te
LbaL In a deductive a.pproach to modeling ration&! agenu.
where a unifonn representa.tion&! forma.lism is used, certain
unusu~ I.JId a.!:,pel.ling.benefits ca.n be gained by integra.ti.ng
deductive effiCIency W1th an assumption ba.sedtruth m&1ntenance .Yltem. The resulting agenL a.rchitecLureis simple,
uniform, bu .impler yeL versatile representations, providing
deductive efficiency as well as &!terna.tea.pproa.ches
Lodel.ling
with the STRIPS a.ssumption.
Bulletin,
2(4):89-92,
August 1991.
[Kuma.r a.nd Shapiro 1991b] Deepak Kuma.r and Stua.rt C.
Shapiro. Modeling a ration&! cognitive agent in SNePS.
In B. B a.ra.hon
a., L. Moniz Pereira., and A. Porto, editors,
EPIA 91: 5th Portuge.e Confe~na on Artificial Intelligena, Lectu~ Note. in Artificial Intelligence 541, pa.ges
120-134. Springer-Verlag, Heidelberg, 1991.
[Muuns and Sba.piro 1988] J. P. Ma.rtins a.ndS. C. Sha.piro.
A model for belief revision.
Artificial Intelligence,
35(1):25-79, 1988.
[Niluon 1980] Nils J. Nilsson. Pnnciple. Of Artificial Intel.
ligence. Tioga Publiahing Compl.JlY, P&!o Alto, CA, 1980.
References
~
[Drumm~nd 1987] ~a.rk E. Drum~ond.
representa.tion
of action a.nd belief for automa.tlc pla.nnlng systems. In
Michael P. Georgeff and Amy L. Lansky, editors, Rea.
.oning aboutAction. and Plan.
I
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I
I
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I
.
[H.uli 1986) R. G. Hull. A new des.lgn for SNIP the SNePS
inference pa.c~e. SNeRG Technic&! Note 14, Depa.rtment
of Computer Saence, SUNY a.t Buffl.lo, 1986.
sbelf planning/acting system. Tbis onl~ resulu in pa.ra.digm
.oups. The appr.~
we ha.ve taken 15 to extend ,the KR
syst~m by extendl~g Its ontology ~d
serVIng Its foundations. The resulting
I
< Mr, {M22!,M3!}, {} >
M26!: ActPrecondition(PICKUP(A),Clear(A))
M29! : ActEt:ect(PICKUP(A), HeId(A))
M30!: ActEt:ect(PICKUP(A),-.Clelr(A)
M9! : Vx, y[lu(x, BLOCK) Alu(y, SUPPORT) A On(x, y)
M2I!:II8(B,BLOCK)
M3.!: ka(B, SUPPORT)
M37!:...on(A,B)
M38!:Clur(B)
M28!: -.Clelr(A)
I
>
[Pinto-Ferreira. et al. 1989] Ca.rl~ Pinto-Ferreira Nunn. J.
Ma.mede, and Jo a.o P. Ma.rtins. SNIP 2.1- The SNePS
Inference Package. Technicl.l Report GIA 89/5, Technic&!
- Proceeding..of the 1986
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I
I
I
I
University of Lisbon, December1989.
I
98
I
.
~~"
-
~,-
'"""~..
..-.
--
I
.;-,-*-~
-"
~ ,_.
[Sha.piro
I
I
,~
J
;~~:,~'.;i~,'~'"
I
-~-..~-"~.=,
.
a.nd Group
1989]
S. C. Sha.piro
a.nd The SNePS
Im-
..
plementa.tion Group.. SNePS-! U,er', Manual. DeputmenL of Computer Science, SUNY a.t Buffa.lo, 1989.
,"C,"
'".. ;~~..i
-
'"-"'""'~;i;-~~;;-:';!M
,';:;.t.J'"~..~
~'?)
; '~~l!
," ~-c-;-.;:;C;1\,}; " ";,,~:~ :{:~!:"""': :t-~~
.. ~};;t: - j~~,~~~::;::({:,~: c~;;
[Sha.piro a.nd Ma.rtina 1989]
S. C. Sha.plro a.nd
J. P. Ml.rt.ina.
_I
h SN PS 2.1 re~Dt
...YaDces a.nd de~opmenia
- tee
n__.J
port. In D. Kuma.r, editor, Cu~t
Trend" in SNePSSemantic Net~on Prvce"ing Sv,tem: Proceeding, of the
Fir,t Annual SNePS Womhop, p&ges 1-13, Buffa.lo, NY,
;~~}OJ;;::,l',i\1.~ ':";";
,'.'. '" -. ,\"";;"2'.;~..:?~~,j~f'jA
"
: ~,""';~A
'~"':-:'~}:,"~~"~~c,A
. 1~':;;!\.t
'!j;~'::'I:JJ:,' !!:\:;;~
"}~~:}~,~T : !",~
1989. Sprinser- Verl~.
[Wilkins 1988J Da.vid E. Wilkin..
Pructirol PlanningEztending the ClG4,irol AI Planning Pamdigm. Morga.n
Ka.ufma.nn,Pa.loAlLo, CA, 1988.
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99
..